We generalize completely prime ideals in rings to submodules in modules. The notion of
multiplicative systems of rings is generalized to modules. Let N be a submodule of a left R …

In this paper, we first investigate the relationships between the McCoy module and related
modules based on their relationships in rings. After that, we improve some properties of …

A relationship between nilpotency and primeness in a module is investigated. Reduced
modules are expressed as sums of prime modules. It is shown that presence of nilpotent …

A notion of 2-primal rings is generalized to modules by defining 2-primal modules. We show
that the implications between rings which are reduced, have insertion-of-factor-property …

In this dissertation, we study the relationships between the notions of a morphic element and
a morphic ring or module on one hand and reduced and regular rings or modules on the …

This thesis is aimed at generalizing notions of rings to modules. In particular, notions of
completely prime ideals, s-prime ideals, 2-primal rings and nilpotency of elements of rings …

For an commutative ring T with identity, we define Distributive ring if any module over T is
distributive. In this paper we study and investigate some new relationships between …

The formal study of completely prime modules was initiated by NJ Groenewald and the
current author in the paper: Completely prime submodules, Int. Electron. J. Algebra, 13 …

In this paper we have introduced the notion of weak reduced module and weak rigid module
as the generalizations of reduced module by working on the context of nilpotent elements of …

We investigate properties of different monoid module radicals arising from the different
definitions of “prime” modules. Let R be a unital ring, M an R-module, and G a monoid. If γ is …